An “offline” approach to DA is used, where static ensemble samples are drawn from existing CMIP climate‐model simulations to serve as the prior estimate of climate variables. We use linear, univariate forward models (“proxy system models (PSMs)”) that map climate variables to proxy measurements by fitting proxy data to 2 m air temperature from gridded instrumental temperature data; the linear PSMs are then used to predict proxy values from the prior estimate. Results for the LMR are compared against six gridded instrumental temperature data sets and 25% of the proxy records are withheld from assimilation for independent verification. Results show broad agreement with previous reconstructions of Northern Hemisphere mean 2 m air temperature, with millennial‐scale cooling, a multicentennial warm period around 1000 C.E., and a cold period coincident with the Little Ice Age (circa 1450–1800 C.E.). Verification against gridded instrumental data sets during 1880–2000 C.E. reveals greatest skill in the tropics and lowest skill over Northern Hemisphere land areas. Verification against independent proxy records indicates substantial improvement relative to the model (prior) data without proxy assimilation. As an illustrative example, we present multivariate reconstructed fields for a singular event, the 1808/1809 “mystery” volcanic eruption, which reveal global cooling that is strongly enhanced locally due to the presence of the Pacific‐North America wave pattern in the 500 hPa geopotential height field.

Abstract. The Last Millennium Reanalysis (LMR) utilizes an ensemble methodology to assimilate paleoclimate data for the production of annually resolved climate field reconstructions of the Common Era. Two key elements are the focus of this work: the set of assimilated proxy records and the forward models that map climate variables to proxy measurements. Results based on an updated proxy database and seasonal regression-based forward models are compared to the LMR prototype, which was based on a smaller set of proxy records and simpler proxy models formulated as univariate linear regressions against annual temperature. Validation against various instrumental-era gridded analyses shows that the new reconstructions of surface air temperature and 500 hPa geopotential height are significantly improved (from 10 % to more than 100 %), while improvements in reconstruction of the Palmer Drought Severity Index are more modest. Additional experiments designed to isolate the sources of improvement reveal the importance of the updated proxy records, including coral records for improving tropical reconstructions, and tree-ring density records for temperature reconstructions, particularly in high northern latitudes. Proxy forward models that account for seasonal responses, and dependence on both temperature and moisture for tree-ring width, also contribute to improvements in reconstructed thermodynamic and hydroclimate variables in midlatitudes. The variability of temperature at multidecadal to centennial scales is also shown to be sensitive to the set of assimilated proxies, especially to the inclusion of primarily moisture-sensitive tree-ring-width records.

[1] The response of the tropical Pacific Ocean to future climate change remains highly uncertain, in part because of the disagreement among observations and coupled general circulation models (CGCMs) regarding 20th-century trends. Here we use forward models of climate proxies to compare CGCM simulations and proxy observations to address 20th-century trends and assess remaining uncertainties in both proxies and models. We model coral oxygen isotopic composition (d 18 O) in a 23-site Indo-Pacific network as a linear function of sea-surface temperature (SST) and seasurface salinity (SSS) obtained from historical marine observations (instrumental data) and a multimodel ensemble of 20th-century CGCM output. When driven with instrumental data from 1958 to 1990, the forward modeled corals (pseudocorals) capture the spatial pattern and temporal evolution of the El Niño-Southern Oscillation (ENSO). Comparison of the linear trend observed in corals and instrumental pseudocorals suggests that the trend in corals between 1958 and 1990 results from both warming (60%) and freshening (40%). From 1890 to 1990, the warming/freshening trend in CGCM pseudocorals is weaker than that observed in corals. Corals display a moderate trend towards a reduced zonal SST gradient and decreased ENSO-related variance between 1895 and 1985, whereas CGCM pseudocorals display a range of trend patterns and an increase in ENSO-related variance over the same period. Differences between corals and CGCM pseudocorals may arise from uncertainties in the linear bivariate coral model, uncertainties in the way corals record climate, undersensitivity of CGCMs to radiative forcing during the 20th century, and/or biases in the simulated CGCM SSS fields.

Paleoclimate observations constitute the only constraint on climate behavior prior to the instrumental era. However, such observations only provide indirect (proxy) constraints on physical variables. Proxy system models aim to improve the interpretation of such observations and better quantify their inherent uncertainties. However, existing models are currently scattered in the literature, making their integration difficult. Here, we present a comprehensive modeling framework for proxy systems, named PRYSM. For this initial iteration, we focus on water-isotope based climate proxies in ice cores, corals, tree ring cellulose, and speleothem calcite. We review modeling approaches for each proxy class, and pair them with an isotopeenabled climate simulation to illustrate the new scientific insights that may be gained from this framework. Applications include parameter sensitivity analysis, the quantification of archive-specific processes on the recorded climate signal, and the quantification of how chronological uncertainties affect signal detection, demonstrating the utility of PRYSM for a broad array of climate studies.